Rate of Change

Rate of Change

I can 
● Determine rate of change from a graph
● Determine the rate of change from a table
● Determine the rate of change from ordered pairs

Labelling

Determine the ordered pairs of the points that are labeled on the graph.

Drag labels to their correct position on the image

(4,6)

(6,0)

(-7,-7)

(0,6)

(6,4)

Rate of Change Lesson

During this lesson, there will be slides that will give you definitions and examples. You should be taking notes during these slide. There will also be slides where you will be asked to answer questions. Please answer the questions to your best ability. 

What is rate of change?

• A constant rate of change is when the rate of change between any two quantities remains the same. This is a linear relationship. 

• The slope is a constant rate of change for a linear relationship. 

Match

Match the graph to the correct description of the rate of change

Positive Rate of Change

Negative Rate of Change

Zero Rate of Change

Undefined Rate of Change

• Positive Rate of Change

• Negative Rate of Change

• Zero Rate of Change

• Undefined Rate of Change

Rate of Change of a graph can be represented by the fraction:

Δy/Δx

Let's find the rate of change of this graph.

1. Find two point on the function (it can be any two points!)

Let's find the rate of change of this graph.

2. From the point on the left draw a vertical line and a horizontal line to connect the two points. (It will look like a triangle!)

Let's find the rate of change of this graph.

3. Find the height of your vertical line. Make sure you are using positive (up) and negative (down) for your direction.

Let's find the rate of change of this graph.

3. Find the length of your horizontal line. Make sure you are using positive (right) and negative (left) for your direction.

Let's find the rate of change of this graph.

3. Find the Δy/Δx. 

Δy = 5, Δx =2.

Δy/Δx= 5/2
Answer = 5/2

Fill in the Blank

Find the rate of change.

Fill in the Blank

Find the rate of change

-

To find the rate of change of a table, determine the pattern of the y values and x values

Δy/Δx

Let's find the rate of change from a table. 

1. Find the change in x. (What do you add or subtract by to get the next value?)

Let's find the rate of change from a table. 

2. Find the change in y. (What do you add or subtract by to get the next value?)

Let's find the rate of change from a table. 

3. Find the (change in y)/(change in x). 

change in y = 10
change in x =2
(change in y)/(change in x) = 10/2
Answer: 5

Let's find the rate of change from a table. 

1. Find the change in x. (What do you add or subtract by to get the next value?)

Let's find the rate of change from a table. 

2. Find the change in y. (What do you add or subtract by to get the next value?)

Let's find the slope from a table. 

3. Find the (change in y)/(change in x). 

change in y = -1
change in x = 6
(change in y)/(change in x) = 6/-1
Answer: -6

Math Response

Find the rate of change.

Type answer here

Correct Answer: -\frac{2}{3}

Deg^°

Rad

Math Response

Find the rate of change

Type answer here

Correct Answer: \frac{4}{3}

Deg^°

Rad

To find the rate of change between two points.

To find the rate of change between two points

1. Identify (x₁, y₁) and (x₂, y₂).

To find the rate of change between two points:

2.Find the change in y
Answer: 2

3. Find the change in x
Answer: 4

4. Simplify
Answer:2/4 = 1/2

Math Response

Find the slope between

$$\left(3,\ 0\right)\ and\ \left(-11,\ -15\right)$$  

Type answer here

Correct Answer: \frac{15}{14}

Deg^°

Rad

Math Response

Find the rate of change between

$$\left(-4,\ 7\right)\ and\ \left(-6,\ -4\right)$$  

Type answer here

Correct Answer: \frac{11}{2}

Deg^°

Rad

Checkpoint

Answer the following questions to check your understanding of this lesson.

Multiple Choice

Which of these graphs has no rate of change?

Math Response

Find the rate of change.

Type answer here

Correct Answer: 2

Deg^°

Rad

Math Response

Find the rate of change

Type answer here

Correct Answer: \frac{4}{3}

Deg^°

Rad